ZURICH, Sept 27 (Reuters) - Sunrise Communications could slash the size of its planned 4.1 billion Swiss franc ($4.13 billion) rights issue to finance its purchase of Liberty Global's Swiss UPC business, four people close to the situation told Reuters.

The Swiss group has been discussing with investors how it could reduce the amount of new equity it would issue to fund the 6.3 billion franc deal, thus breaking down resistance to the transaction by its biggest shareholder, Freenet.

The preferred version would reduce the equity part to around 3 billion francs or even less, the people said. The final details should emerge in coming days when Sunrise invites shareholders to an extraordinary meeting on Oct. 23 to approve the capital increase.

Sunrise wants UPC to win market share and bulk up against market leader Swisscom. But it is unclear whether a significantly smaller rights issue would be enough to win over investors wary about the price and deal structure.

Sunrise has said it is confident it will get the simple majority it needs at the EGM to move ahead. "A majority of our investors are behind this transaction," the company said on Friday.

Sources familiar with the matter also said Freenet has also been wooing Sunrise investors, to get them to oppose the original plans for a rights issue worth more than Sunrise's market capitalisation.

In the fight for every vote, the recommendations of proxy advisers could play an important role. Many foreign institutional investors follow their advice.